Add traits for generic norms and distances.

[Nuramon27]

In many iterative numerical algorithms, one has to calculate the distance between a solution candidate and a reference value in order to check for convergence. But currently there is no trait which would enable the computation of such a distance generically.

There is Signed which provides an abs function, but this trait can only be implemented for types with a notion of signedness. The correct mathematical concept, however, are norms and metrics, with the latter being reasonable for basically any numeric type.

So I propose adding two traits, Norm and Distance, each with one method of the same name. The norm-function of the Norm trait returns the norm of a single value, the distance-function of the Distance trait returns the distance between two values.

In my branch dist I have written a draft of these traits and implemented them for the primitive numeric types.

[cuviper]

It's a reasonable idea. Can you open it as a PR for discussion?

One thing to consider is that there are multiple possible definitions of norm, especially when more dimensions are added like in Complex<T>. e.g. Euclidean norm vs. Manhattan norm.

[JohnScience]

It's a reasonable idea. Can you open it as a PR for discussion?

One thing to consider is that there are multiple possible definitions of norm, especially when more dimensions are added like in Complex<T>. e.g. Euclidean norm vs. Manhattan norm.

Are you sure that it must be the responsibility of num-traits?
Creating another managed crate (for example, "num-maths-traits") which would contain category-, group-, field-, ring-, space-, and other more general traits sounds a better idea. In this case, trait inheritance from more general traits can be an opt-in feature enabled by default.

The problem is not even that num-traits may end up becoming too of a heavy dependency in attempts to fit all needs but that num-traits' purpose statement ("Numeric traits for generic mathematics in Rust"), would, in this case, become unclear to me and, perhaps, someone else.

[cuviper]

Are you sure that it must be the responsibility of num-traits?

Not at all. If there are interested parties like yourself who want to explore this in a new crate (and not get bogged down in num-traits' conservative API), then feel free!